Question

15. The length of a rectangle is 5 cm more than 4 times the width. If the perimeter of the rectangle is 50 cm,what are its dimensions? (The perimeter of a rectangle is twice the sum of the length and the width.)

Answer 1

Step 1: Write out the formula for the perimeter of a rectangle

`\begin{gathered} P=2(l+w) \\ \text{ Where} \\ P=\text{ the perimeter} \\ l=\text{ the length} \\ w=\text{ the width} \end{gathered}`

Step 2: Write out the given value and substitute them into the formula above

`\begin{gathered} \text{ The length of the rectangle is 5cm more than 4 times the width} \\ \text{therefore} \\ l=4w+5----(1) \\ \text{ the perimeter is 50cm} \\ \text{Hence} \\ 2(l+w)=50 \\ l+w=25---(2) \end{gathered}`

Substituting equation (1) into equation (2), we have

`\begin{gathered} (4w+5)+w=25 \\ 4w+w=25-5 \\ 5w=20 \\ (5w)/(5)=(20)/(5) \\ w=4cm \end{gathered}`

Substituting the value of w into equation(1), we have

Hence, the length is 21 cm and the width is 4cm